{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T18:28:43Z","timestamp":1780338523157,"version":"3.54.1"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,6,4]],"date-time":"2022-06-04T00:00:00Z","timestamp":1654300800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,6,4]],"date-time":"2022-06-04T00:00:00Z","timestamp":1654300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000765","name":"University College London","doi-asserted-by":"publisher","award":["UCL CBT"],"award-info":[{"award-number":["UCL CBT"]}],"id":[{"id":"10.13039\/501100000765","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["EPJ Data Sci."],"published-print":{"date-parts":[[2022,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Reaching consensus\u2014a macroscopic state where the system constituents display the same microscopic state\u2014is a necessity in multiple complex socio-technical and techno-economic systems: their correct functioning ultimately depends on it. In many distributed systems\u2014of which blockchain-based applications are a paradigmatic example\u2014the process of consensus formation is crucial not only for the emergence of a leading majority but for the very functioning of the system. We build a minimalistic network model of consensus formation on blockchain systems for quantifying how central nodes\u2014with respect to their average distance to others\u2014can leverage on their position to obtain competitive advantage in the consensus process. We show that in a wide range of network topologies, the probability of forming a majority can significantly increase depending on the centrality of nodes that initiate the spreading. Further, we study the role that network topology plays on the consensus process: we show that central nodes in scale-free networks can win consensus in the network even if they broadcast states significantly later than peripheral ones.<\/jats:p>","DOI":"10.1140\/epjds\/s13688-022-00347-5","type":"journal-article","created":{"date-parts":[[2022,6,4]],"date-time":"2022-06-04T12:02:54Z","timestamp":1654344174000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Consensus formation on heterogeneous networks"],"prefix":"10.1140","volume":"11","author":[{"given":"Edoardo","family":"Fadda","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junda","family":"He","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7733-6221","authenticated-orcid":false,"given":"Claudio J.","family":"Tessone","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4588-667X","authenticated-orcid":false,"given":"Paolo","family":"Barucca","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,6,4]]},"reference":[{"key":"347_CR1","doi-asserted-by":"publisher","unstructured":"Tasca P, Tessone CJ (2019) A taxonomy of blockchain technologies: principles of identification and classification. Ledger 4. https:\/\/doi.org\/10.5195\/ledger.2019.140","DOI":"10.5195\/ledger.2019.140"},{"issue":"2","key":"347_CR2","doi-asserted-by":"publisher","DOI":"10.1098\/rsos.172189","volume":"5","author":"A Baronchelli","year":"2018","unstructured":"Baronchelli A (2018) The emergence of consensus: a primer. R Soc Open Sci 5(2):172189","journal-title":"R Soc Open Sci"},{"key":"347_CR3","doi-asserted-by":"crossref","unstructured":"Tessone C, Tasca P, Iannelli F (2021) Stochastic modelling of blockchain consensus. Available at SSRN 3865040","DOI":"10.2139\/ssrn.3865040"},{"key":"347_CR4","unstructured":"Nakamoto S (2009) Bitcoin: a peer-to-peer electronic cash system"},{"key":"347_CR5","doi-asserted-by":"publisher","DOI":"10.3389\/fbloc.2020.613476","volume":"3","author":"F Spychiger","year":"2021","unstructured":"Spychiger F, Tasca P, Tessone CJ (2021) Unveiling the importance and evolution of design components through the \u201ctree of blockchain\u201d. Front Blockchain 3:613476","journal-title":"Front Blockchain"},{"key":"347_CR6","doi-asserted-by":"publisher","first-page":"43620","DOI":"10.1109\/ACCESS.2021.3065880","volume":"9","author":"B Lashkari","year":"2021","unstructured":"Lashkari B, Musilek P (2021) A comprehensive review of blockchain consensus mechanisms. IEEE Access 9:43620\u201343652","journal-title":"IEEE Access"},{"key":"347_CR7","doi-asserted-by":"publisher","first-page":"2567","DOI":"10.1109\/SMC.2017.8123011","volume-title":"2017 IEEE international conference on systems, man, and cybernetics (SMC)","author":"D Mingxiao","year":"2017","unstructured":"Mingxiao D, Xiaofeng M, Zhe Z, Xiangwei W, Qijun C (2017) A review on consensus algorithm of blockchain. In: 2017 IEEE international conference on systems, man, and cybernetics (SMC), pp\u00a02567\u20132572. https:\/\/doi.org\/10.1109\/SMC.2017.8123011"},{"key":"347_CR8","first-page":"1","volume-title":"IEEE P2P 2013 proceedings","author":"C Decker","year":"2013","unstructured":"Decker C, Wattenhofer R (2013) Information propagation in the Bitcoin network. In: IEEE P2P 2013 proceedings. IEEE, pp\u00a01\u201310"},{"key":"347_CR9","doi-asserted-by":"crossref","unstructured":"Stifter N, Schindler P, Judmayer A, Zamyatin A, Kern A, Weippl E (2019) Echoes of the past: recovering blockchain metrics from merged mining, pp\u00a01\u201323","DOI":"10.1007\/978-3-030-32101-7_31"},{"key":"347_CR10","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1007\/978-3-662-45472-5_28","volume-title":"International conference on financial cryptography and data security","author":"I Eyal","year":"2014","unstructured":"Eyal I, Sirer EG (2014) Majority is not enough: Bitcoin mining is vulnerable. In: International conference on financial cryptography and data security. Springer, Berlin, pp\u00a0436\u2013454"},{"key":"347_CR11","doi-asserted-by":"publisher","first-page":"156","DOI":"10.1109\/ICCCWorkshops49972.2020.9209934","volume-title":"2020 IEEE\/CIC international conference on communications in China (ICCC workshops)","author":"S-N Li","year":"2020","unstructured":"Li S-N, Yang Z, Tessone CJ (2020) Proof-of-work cryptocurrency mining: a statistical approach to fairness. In: 2020 IEEE\/CIC international conference on communications in China (ICCC workshops). IEEE, pp\u00a0156\u2013161"},{"key":"347_CR12","first-page":"1","volume-title":"2020 IEEE international conference on blockchain and cryptocurrency (ICBC)","author":"S-N Li","year":"2020","unstructured":"Li S-N, Yang Z, Tessone CJ (2020) Mining blocks in a row: a statistical study of fairness in Bitcoin mining. In: 2020 IEEE international conference on blockchain and cryptocurrency (ICBC). IEEE, pp\u00a01\u20134"},{"key":"347_CR13","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1109\/BCCA53669.2021.9657011","volume-title":"2021 third international conference on blockchain computing and applications (BCCA)","author":"C Schwarz-Schilling","year":"2021","unstructured":"Schwarz-Schilling C, Li S-N, Tessone CJ (2021) Agent-based modelling of strategic behavior in pow protocols. In: 2021 third international conference on blockchain computing and applications (BCCA). IEEE, pp\u00a0111\u2013118"},{"key":"347_CR14","doi-asserted-by":"crossref","unstructured":"Neudecker T, Hartenstein H (2019) Short paper: an empirical analysis of blockchain forks in Bitcoin, pp\u00a01\u20138","DOI":"10.1007\/978-3-030-32101-7_6"},{"key":"347_CR15","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1007\/978-3-662-53357-4_8","volume-title":"International conference on financial cryptography and data security","author":"K Croman","year":"2016","unstructured":"Croman K, Decker C, Eyal I, Gencer AE, Juels A, Kosba A, Miller A, Saxena P, Shi E, Sirer EG et al. (2016) On scaling decentralized blockchains. In: International conference on financial cryptography and data security. Springer, Berlin, pp\u00a0106\u2013125"},{"key":"347_CR16","doi-asserted-by":"crossref","unstructured":"Shahsavari Y, Zhang K, Talhi C (2019) Performance modeling and analysis of the Bitcoin inventory protocol","DOI":"10.1109\/DAPPCON.2019.00019"},{"key":"347_CR17","unstructured":"Shahsavari Y, Zhang K, Talhi C A theoretical model for fork analysis in the Bitcoin network"},{"issue":"6","key":"347_CR18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.76.066101","volume":"76","author":"VD Blondel","year":"2007","unstructured":"Blondel VD, Guillaume J-L, Hendrickx JM, Jungers RM (2007) Distance distribution in random graphs and application to network exploration. Phys Rev E 76(6):066101","journal-title":"Phys Rev E"},{"key":"347_CR19","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1002\/9781119519621.ch3","volume-title":"Blockchain for distributed systems security","author":"M Saad","year":"2019","unstructured":"Saad M, Spaulding J, Njilla L, Kamhoua CA, Nyang D, Mohaisen A (2019) Overview of attack surfaces in blockchain. In: Blockchain for distributed systems security, pp\u00a051\u201366"},{"key":"347_CR20","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1109\/EMPDP.2019.8671550","volume-title":"Proceedings\u201427th euromicro international conference on parallel, distributed and network-based processing, PDP 2019","author":"M Geier","year":"2019","unstructured":"Geier M, Tessone CJ, Vanotti M, Vileri\u00f1o S, M\u00e1rquez DG, Mocskos E (2019) Using network emulation to study blockchain distributed systems: the Ethereum case. In: Proceedings\u201427th euromicro international conference on parallel, distributed and network-based processing, PDP 2019, pp\u00a051\u201358. https:\/\/doi.org\/10.1109\/EMPDP.2019.8671550"},{"key":"347_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/icbc48266.2020.9169436","volume-title":"2020 IEEE international conference on blockchain and cryptocurrency (ICBC)","author":"L Sheng-Nan","year":"2020","unstructured":"Sheng-Nan L, Zhao Y, Claudio JT (2020) Mining blocks in a row: a statistical study of fairness in Bitcoin mining. In: 2020 IEEE international conference on blockchain and cryptocurrency (ICBC), pp\u00a01\u20134. https:\/\/doi.org\/10.1109\/icbc48266.2020.9169436. https:\/\/doi.org\/10.5167\/uzh-193491"},{"key":"347_CR22","doi-asserted-by":"crossref","unstructured":"Gervais A (2016) On the security, performance and privacy of proof of work blockchains. PhD thesis, ETH, Zurich","DOI":"10.1145\/2976749.2978341"},{"key":"347_CR23","unstructured":"L\u00fctkebohle I (2022) Y charts Ethereum uncle rate. https:\/\/ycharts.com\/indicators\/ethereum_uncle_rate [Online; accessed 14-March-2022]"},{"key":"347_CR24","volume-title":"Network science","author":"A-L Barab\u00e1si","year":"2016","unstructured":"Barab\u00e1si A-L, P\u00f3sfai M (2016) Network science. Cambridge University Press, Cambridge. http:\/\/barabasi.com\/networksciencebook\/"},{"issue":"4\u20135","key":"347_CR25","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/j.physrep.2005.10.009","volume":"424","author":"S Boccaletti","year":"2006","unstructured":"Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D-U (2006) Complex networks: structure and dynamics. Phys Rep 424(4\u20135):175\u2013308. https:\/\/doi.org\/10.1016\/j.physrep.2005.10.009","journal-title":"Phys Rep"},{"key":"347_CR26","doi-asserted-by":"publisher","first-page":"57009","DOI":"10.1109\/access.2019.2914098","volume":"7","author":"S Park","year":"2019","unstructured":"Park S, Im S, Seol Y, Paek J (2019) Nodes in the Bitcoin network: comparative measurement study and survey. IEEE Access 7:57009\u201357022. https:\/\/doi.org\/10.1109\/access.2019.2914098","journal-title":"IEEE Access"}],"container-title":["EPJ Data Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1140\/epjds\/s13688-022-00347-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1140\/epjds\/s13688-022-00347-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1140\/epjds\/s13688-022-00347-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,7]],"date-time":"2023-02-07T08:14:03Z","timestamp":1675757643000},"score":1,"resource":{"primary":{"URL":"https:\/\/epjdatascience.springeropen.com\/articles\/10.1140\/epjds\/s13688-022-00347-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,4]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,12]]}},"alternative-id":["347"],"URL":"https:\/\/doi.org\/10.1140\/epjds\/s13688-022-00347-5","relation":{},"ISSN":["2193-1127"],"issn-type":[{"value":"2193-1127","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,4]]},"assertion":[{"value":"29 November 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 May 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 June 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"34"}}